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## An Approach## to## CALCULUSThe Lessons 11. Continuous versus discrete 12. Limits A sequence of rational numbers. The limit of a variable. The continuity of the The definition of "continuous at a point." The definition of "becomes infinite." Limits of rational functions. 15. The derivative The slope of a tangent line to a curve. The difference quotient and the definition of the derivative. Differentiability. Notations for the derivative. The derivative of a constant. The derivative of 17. The chain rule The derivative of a function of a function. 18. More rules for derivatives The quotient rule. 19. Velocity and rates of change Instantaneous velocity. 10. Maximum and minimum values The turning points of a graph. Critical values. 11. Applications of maximum and minimum values 12. Derivatives of trigonometric functions 13. Derivatives of inverse trigonometric functions 14. Derivatives of exponential and logarithmic functions Exponential growth. The system of natural logarithms. The general power rule. 15. Evaluating
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